Resistance element



June 17, 1941. COLLAR]: 2,246,293 RESISTANCE ELEMENT Filed May 6, 1939 INV EN TOR. JOHN C'OLLARD ATTORNEY.

Patented June 17, 1941 2,246,293 RESISTANCE ELEMENT John Collard,Hammersmith, London, England,

assignor to Electric & Musical Industries Limited, Hayes, Middlesex,England, a company of Great Britain Application May 6, 1939, Serial No.272,189v

In Great Britain May 12, 1938 7 Claims. (Cl. 17844) This inventionrelates broadly to impedance elements that are required in impedancenetworks to appear substantially as constant resistances over a range offrequencies from zeroto quite high frequencies, or are such as to -haveduced, wherein for the purpose of substantially in an impedance networkand for a given purpose the same effect as constant resistances. Moreparticularly, though not exclusively, this invention relates to the use.of such impedances in an attenuator network for use at highfrequencies. 2 In the specification of British Patent No.

362,472 an attenuator in the form of an artificial line constructed ofvr-type sections isv described suitable for transmitting with modifiedamplitude a potential from a source to a ,load. As described, theattenuator is suitable for use only at frequencies for which theresistances that form its structure remain pure resistances, and atwhich the effect of stray capacities and inductances in the attenuatorare of negligibly small effect. At frequencies of the order of 1megacycle per second it is difiicult to obtain res stances suitable foruse in such an attenuator, which are both stable and non-inductive. Alsoat such frequencies the effect of stray capacities in the attenuator isliable to cause the attnua} tion to depart from the intended value.

It is one object of the invention to overcome or reduce thesedifiiculties and defects in such an attenuator when it is operated athigh frequencies.

According to one feature of the invention there is provided anelectrical network for use over a wide range of frequencies comprisingimpedance e ements required to appear resistive over said 5 range to ahigh degree of accuracy, but possessing inductance and capacity to adegree such that at least at the higher frequencies of said rangeappreciable inductive and capacitative reactances are introduced,wherein for the purpose eliminating the effect of these reactances theinductance capacity and resistance, L, C and R respectively of saidimpedance element are so chosen as to satisfy substantially thecondition L/C= /2R and a reactive element possessing properties chosenin nature and magnitude with regard to those of said impedance elementis so associated with said impedance element that said impedance elementappears as a substantially constant resistance throughout said range.

In order that the said invention may be better understood and morereadily carried into effect, the same will now be described by way of example with reference to the accompanying drawing, in which:

Figure 1 illustrates a single section of an attenuator such as has beenreferred to above;

, Figure 2 illustrates-the character of a resistive element in such .anattenuator at high frequencies; Y

Figure 3 shows a circuit in theoretical form that may be applied toovercome the effect of small variations with frequency of the imageimpedance of an attenuator due to small variations of the impedanceofits resistive elements;

Figure 4 shows a practical elaboration of the circuit illustrated inFigure 3;

Figures 5, 6 and '1 illustrate ways in which by suitablyassociatin'g'reactive impedances with a resistive element thecapacitative and inductive of substantially eliminating the effect ofthese reactances the inductance and capacity of said elements are sorelated to the respective resistance of said elements and the inductanceand resistance of each element is so proportioned with respect to thesame properties in the remainder of said elements that said effect issubstantially eliminated.

According to another feature of the invention, there is provided anelectrical network for use over a wide range of frequencies comprisingan impedance element possessing inductance and capacity to a degree suchthat at least at the higher frequencies of said range appreciableinductive and capacitative reactances are introproperties'of-the elementmay be rendered of substantially inappreciable effect;

Figure -8 shows an arrangement by which the stray capacity of leads to aresistive element may be effectively removed, and

Figures 9 and 10 show the equivalent electrical circuits when a sourceand load respectively are connected to an apparatus such as anattenuator.

In order that the description with respect to the above mentioneddrawing may be the better appreciated, the more important features ofthe type of attenuator described in the aforementioned British patentspecification will be first briefly referred to. Such an attenuator maybe regarded as a semi-infinite line provided, of course, that the farend of the attenuator is correctly terminated. In use a source (or aload impedance) is connected to the near end and a load impedance (or asource) is connected across the line at some tapping point along itslength. By altering the position of this point the attenuation betweenthe source and the load may be changed. ihe tapping point is shifted infinite steps corresponding to whole sections in the attenuator, so thatif the attenuation of the separate sections is known changes inattenuation may be measured. The attenuation may, however, only bemeasured in this way provided either the impedance connected across thenear end of theline is equal to the characteristic impedance of theline, or the impedance connected across the line at the tapping point isvery high compared with the characteristic impedance of the line; boththese conditions, of course, may be satisfied simultaneously. In thefollowing it will be assumed that the attenuator is used in accordancewith the foregoing conditions.

Referring to Figure l, the resistance A is the series element and theresistances B, B are the shunt elements of a single 1r section of theattenuator. The impedances connected across the ends of the sectionindicate that the section is correctly terminated at either end in itscharacteristic impedance Z0. When this is so a potential difference V1applied across one end of the section will give rise at the other end toa potential difference BZ AB+ AZ,,+BZ,,

In order that the attenuator should function correctly it is necessary,as is clear from the above equation, that the resistances A and B shouldbehave as pure and constant resistances.

It is possible to achieve this condition even at quite high frequenciesby using resistances of the so-called chemical-type in which a thinconducting filmis deposited on a small rod of glass or otherinsulatingmaterial, as these have very small inductances' and capacity, but suchresistances are subject to random variations which make them unsuitablefor use in accurate apparatus. Accordingly it is preferable to employresistances of the non-inductive wire wound type and providecompensating means to correct for their residual inductance and straycapacity. Such resistances have besides their stability the furtheradvantage overthe chemical type, that they possess a comparatively smalltemperature coefiicient.

Figure 2 indicates diagrammatically how such a non-inductive wire woundresistance must be regarded at high frequencies of the order of 1megacycle per second. In series with the resistance R there is theresidual inductance L and across these there is the effective straycapacity C. The impedance of this combination is given by the expressionIf it is arranged that then for frequencies at which w LC is negligiblysmall compared with unity the expression reduces simply to R. However,the range of values of resistance required in an attenuator of the kindhere considered is such as to render it impossible that for everyresistance the magnitude of w LC should be small compared with unity.

One manner in which according to the invention this difiiculty isovercome is as follows: If #0 110 is not negligible compared with unitythen the above expression reduces not to R, but to the expression and isof theorder of 0.1. To the order of accuracy that is required inmeasurement, since k =w LC it follows that k is not a negligibly smallquantity. However, k will be of the order of 0.001 which may be taken asnegligible and so the above expression in k may be written more simplyas is, according to the invention, made the same for all resistances inthe attenuator. With this arrangement the value of k is identical forall resistances at all frequencies. Even if, therefore, the magnitude ofcomparatively highpowers of k: is not negligible compared with unity,the attenuator will give the same attenuation as it does at lowfrequencies where .no complications due to I residual inductance andstray capacity arise. Thus if and -tan 0=lc the impedance of any of theresistance elements in the attenuator can be expressed in the form: RM10 so that in terms of V1 the potential difference V2 is given accordingto the equation:

In this way it will be seen the attenuation is rendered independentoffrequency by the fulfilling of two conditions, namely:

(a) That shall have identical values for all resistances;

(b) That with all resistances the value of amazes manner across theresistance until the-correct ratio of I is obtained.

If the method just described is carried into effect it will beappeciated that the characteristic impedance of the attenuator will nolonger be simply Z at high frequencies but will be given by Z=ZOM L 0.If therefore the attenuator is being used in the condition where thesource connected to the near end of they a tenuator should besubstantially matched to the input impedance of the attenuator thepotential difference applied across the input ofthe attenuator will bedependent upon the frequency. Thus if a source of internal impedance Z0and electromotive force e is employed thepotential difference applied tothe attenuator-will"begiven by the expression and if the ratio isdesignated by k then the: impedance of: the device is expressible aswhich, provided k is negligibly small compared with unity, reduces to Itwill be seen, therefore, that theiimpedance of the attenuator and theshunting device may be written respectively as:

provided the cubes of the terms in t are neg ligible compared withunity, and accordingly the impedance of the combination ZZ Z Z may bewritten RZ R+Zn+kZoki By making hy li k Z the impedance of thecombination, therefore, becomes to a highdegree of accuracy simply butby making R sufficiently large the apparent impedance of the attenuatormay be made to approach as nearly to Z0 as desired. Alternatively, ofcourse, the source impedance may be reduced from Z0 to or the attenuatormay be designed in the first place to have a rather higher impedance, sothat when shunted by the device the resultant impedance is substantiallythat of the source.

In carrying the above method for correcting for the impedance variationof the attenuator into effect, it is preferable to adopt a slightmodification, on account of the fact that the resistance R in theshunting device shown in Figure 3, requires to be a pure resistance andto be independent of frequency. This modification is indicated in thearrangement of Figure 4 which is identical with that of Figure 3, exceptthat the pure resistance R is replaced by the equivalent circuit,namely, a resistance R. in series with a residual inductance L, thesebeing shunted by a capacity C, by which a typical non-inductiveresistance must be represented at high frequencies. The analysis forthis case is similar to that already given except that R must bereplaced by the expression:

1 k3 where and provided that The impedance of the whole device isthereby modified to but this may be written with suflicient accuracy i1+ r he modification, therefore, amounts to replacthere is now obtainedthe relation and from this kz'may be determined since k1,

k3,Rand Z are known quantities. V

This device is used to give the attenuator a constant impedance Z0at-the point at which it is tapped across, into which the source ofimpedance Z is to work; if, therefore, the point at which the source istapped across the attenuator is varied, the point at whichthe'correcting device is tapped across must be correspondingly alteredso that the device is always across the attenuator at the same point asthe source.

Another method in accordance with the invention by which measurementswith the attenuator may be rendered independent offrequency at highfrequencies and thereby reliable at 'such frequencies, will now bedescribed. Broadly speaking, this method comprises adding reactiveimpedances to the resistance elements in the attenuator in such a waythat these elements are made to appear substantially pure constantresistances.

- R i asbefore, but in deriving whichequation it has been supposed that1 1 3 I q The impedance Z2 of;theremaining portion is expressible simplyaccording to Z2=R(1+7'k) and it will be clear if k and k are very smallcompared with unity, then the total impedance Z1+Zz is equal merely to2R. It will be appreciated that this method is an improvement on thesimple method of connecting a capacity 0 across the whole resistance Rand arranging that t- V since with this procedure the impedance dependsmostly on k through a square term, but in the improved method theimpedance depends on k mostly through a cubic term. and is therefore,less susceptible to changes in frequency.

An even better method can be obtained by means of the arrangement shownin Figure 6. In this case as in the previous case there is a resistanceR in series with a residual inductance L, across both of these in seriesthere being connected a capacity C, but instead of a further resistanceR and inductance L being connected in series, there is connected aparallel combination of an inductance L and a capacity 0. As before itis arranged that I and with this restriction and writing the impedanceof the whole arrangement can be expressed as Here be seen that the leastpower of k involvedis as high as the fourth power, whereasin theprevious case the least power was onlythe third power V. L

It may e pointed out that the device shown in Figure 3' and describedabove, may also be used in renderingindividual resistance elementssubstantially independent of frequency. a v

This may be done by connecting it in" shunt with any given resistance.

To. any of the compensating arrangements that have been described aboveit will be realized that there are of course, equivalents of an inversecharacter. Thus it is well known that two networks may be constructedhaving impedances Z1 and'Zz'which satisfy such a relation as Z1Z2 =ZoWhere Z0 is a constant, provided the individual elements of the networksare arranged and related in certain definite ways. Such networks aresaid to be inverse to each other withrespect to Z and. as an examplethere is shown in Figure '7 an arrangement which is such an inverse ofthat illustrated in-Figure 6. -In this arrangement the series portion inFigure 6 comprising the inductance L and the capacity C in parallel hasbeen transformed to a parallel branch in Figure 7, comprising thecapacity in parallel. Thus each group of elements in one arrangement hasits inverse in the other, the inverses being taken with respect to R, sothat the impedances'of such mutually inverse groups satisfy conditionsof-the form Z11 Z21=R and in particular if Z1, Z2 signify the impedancesof the whole networks of Figures 6 and '7 respectively, these willsatisfy Z1Z2=R2. Since, however, Z1 is a very close approximation to theconstant value R it follows that Z2 is an equally close approximation tothe same value. In the same kind of way the inverses to the otherarrangements described may beconstructed.

It wi1l','of course; be appreciated in all the above cases, wherever'acapacity is shown across an element, that this capacity may be partly orwholly constituted by the self capacity of the element.

When the method of rendering each element in the attenuatorsubstantially a constant resistance is adopted,'it is necessary to takeprecautions vagainst the efiect of the stray capacity of leads connectedto the elements. A way of eliminating the effect of such stray capacityis indicated in the arrangement shown in Figure 8.

B1 and R2 in this figure are two identical resistances of magnitude Rwhich have been made substantially independent of frequency by any ofthe methods described above. C1 and C2 represent stray capacities, andthese by the suitable addition of capacity are adjusted to the samevalue C. R1 and R2 are joined together directly at one end andindirectly through the inductance L at the other end. The method thenconsists in so choosing the magnitude of the inductance L that theefiects of the capacities C1 and C2 are eliminated to a substantialwhich if k may be regarded as a negligibly small quantity, becomessimply R.

In the case of an attenuator in which an arm moves over a series ofstuds in order to make contact with any required point on theattenuator, the capacity of this arm to earth must be taken into accountsince otherwise it will cause the attenuation to vary with frequency.The problem is different from that of other stray capacitors in theattenuator in that the stray capacity of the arm moves from point topoint along the attenuator according to the position of the arm.Furthermore, the cable, lead or conductor used to connect the attenuatorto the source will have a certain inductance and capacity and it ispossible at some frequencies that the inductance of the cable mayresonate with the capacity of the attenuator and so cause errors. Thismay be avoided in the manner indicated in Figure 9.

In this figure there is shown a source of electromotive force 6 ofinternal impedance Zu which is equal to the impedance of the attenuator,and this source is connected to the attenuator through a cable ofinductance L. The capacity C shown in the figure represents the capacityof the cable together with that of the moving arm of the attenuator. Ifthe effects of the inductance L and capacity C were absent the potentialdifference V developed across the attenuator would be /26. In actualfact V is given by It may, however, be reduced in value to /28, provideda term in a may be neglected, if the length of the cable is so arrangedthat In this way errors due to the stray capacity of the moving arm andto the inductance of the cable may be subtantially removed. v

A similar difliculty arises in connecting to the attenuator the loadimpedance, which may be a valve voltmeter. In this case the circuitappears as shown in Figure 10. Z0 represents the output impedance of theattenuator and this is in series with the effective generator ofelectromotive force e. C represents the stray capacity of the attenuatorarm and the capacity of the valve voltmeter whose input impedance ismainly capacitative, while L is in the inductance of the cableconnecting the valve voltmeter to the attenuator. The capacity of themoving arm and of the voltmeter are regarded as being located at onepoint as the length of the cable is short.

Owing to the effect of the inductance L and the capacity C the potentialdifference across the valve voltmeter is not equal to e, but given y(It-(c +jZwC By arranging, however, that L 1 c i and neglecting asbefore the term in at, V reduces to e, so that by choosing the correctlength of cable to satisfy this equation the effects of the inductanceof the cable and of the capacity of the valve voltmeter may be made tocancel out.

It will be appreciated that although the methods described in thisspecification have been with special reference to an attenuator for highfrequencies particularly to an attenuator as described in thespecification of British Patent No. 362,472, they are not of suchlimited application, and may clearly be applied to other pieces ofapparatus, for example, a resistance box, which require resistances thatare non-inductive to a high degree at high frequencies.

I claim:

1. An electrical network comprising a plurality of resistances, eachhaving distributed capacity and distributed inductance, and means tomake the ratio of inductance to resistance of each resistance equal to asingle predetermined value and for making the ratio of inductance tocapacity proportional to the second power of a corresponding resistance,the proportionality factor being identical for all resistances.

2. An electrical network comprising a plurality of resistances, eachhaving distributed capacity and distributed inductance, and means tomake the ratio of inductance to resistance of each resistance equal to asingle predetermined value and for making the ratio of inductance tocapacity equal to the second power of the corresponding resistance.

3. An electrical network comprising a plurality of resistances, eachhaving distributed capacity and distributed inductance, and means tomake the ratio of inductance to resistance of each resistance equal to asingle predetermined value and for making the ratio of inductance tocapacity equal to one-half of the second power of the correspondingresistance.

4. An electrical attenuating network comprising a plurality ofresistances associated with capacity and inductance, in which the ratioof in ductance to its associated resistance for all resistances issubstantially identical and in which the ratio of the inductance tocapacity associated with each resistance is equal to the square of theassociated resistance.

5. An electrical attenuating network comprising a plurality ofresistances associated with capacity and inductance, in which the ratioof inductance to its associated resistance for all resistances issubstantially identical and in which the ratio of the inductance tocapacity associ--' ated with each resistance is proportional to thesecond power of a corresponding resistance, the proportionality factorbeing substantially identical for all resistances. v V

6. An electrical attenuating network comprising a plurality ofresistances associated with capacity and inductance, in which the ratioof inductance to its associated resistance for all resistances issubstantially identical and .in which the ratio of the inductance tocapacity associated with each resistance is equal to ,onei half of thesquare of the associated resistance..-

7. In an attenuator having a plurality of resistances, each resistancehaving associated therewith capacity and inductance, the method ofproviding a substantially pure resistive eat-H proportionality factorbeing identical for all re-.

sistances. :V

JOHN COLLARD.

